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Fast Training of Convolutional Networks through FFTs [article]

Michael Mathieu, Mikael Henaff, Yann LeCun
<span title="2014-03-06">2014</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Training a large convolutional network to produce state-of-the-art results can take weeks, even when using modern GPUs.  ...  Convolutional networks are one of the most widely employed architectures in computer vision and machine learning.  ...  Discussion and Future Work We have presented a simple and fast algorithm for training and inference using convolutional networks.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1312.5851v5">arXiv:1312.5851v5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4dh6cvfcxjhmdpk5u6puwcedle">fatcat:4dh6cvfcxjhmdpk5u6puwcedle</a> </span>
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Fast Fourier Transformation for Optimizing Convolutional Neural Networks in Object Recognition [article]

Varsha Nair, Moitrayee Chatterjee, Neda Tavakoli, Akbar Siami Namin, Craig Snoeyink
<span title="2020-10-08">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
More specifically, we implement the FFT-based convolutional neural network to improve the training time of the network.  ...  This paper proposes to use Fast Fourier Transformation-based U-Net (a refined fully convolutional networks) and perform image convolution in neural networks.  ...  The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.04257v1">arXiv:2010.04257v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/6jz7s3li2jdnhph6vh6fjvwqxq">fatcat:6jz7s3li2jdnhph6vh6fjvwqxq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201024092050/https://arxiv.org/pdf/2010.04257v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7f/4a/7f4a097a5ea962c5635d8ce7d06b0ce84e6fa249.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2010.04257v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Very Efficient Training of Convolutional Neural Networks using Fast Fourier Transform and Overlap-and-Add [article]

Tyler Highlander, Andres Rodriguez
<span title="2016-01-25">2016</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Convolution can be efficiently performed as a Hadamard product in the frequency domain. The bottleneck is the transformation which has a cost of O(N^2_2 N) using the fast Fourier transform (FFT).  ...  Convolutional neural networks (CNNs) are currently state-of-the-art for various classification tasks, but are computationally expensive.  ...  Mateen Rizki of Wright State University for the helpful discussions, and the Air Force Office of Scientific Research (AFOSR) for providing the main funding for this work through LRIR 14Y06COR.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1601.06815v1">arXiv:1601.06815v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/z6y4gtyzinf7zm7mgbrhzi75ra">fatcat:z6y4gtyzinf7zm7mgbrhzi75ra</a> </span>
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Detection of EEG Signal Post-Stroke Using FFT and Convolutional Neural Network

Esmeralda C. Djamal, Widiyanti Isni Furi, Fikri Nugraha
<span title="2019-10-01">2019</span> <i title="Institute of Advanced Engineering and Science"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/jechwbgc2vf45k5gxfzblheir4" style="color: black;">Proceeding of the Electrical Engineering Computer Science and Informatics</a> </i> &nbsp;
This study investigates EEG signal detection in post-stroke patients using Fast Fourier Transform (FFT) and 1D Convolutional Neural Network (1D CNN).  ...  Although both provide training data accuracy of 100%, the accuracy of training data is very dependent on variations in training data.  ...  Deep learning is part of machine learning with increased accuracy. This method used depth computing through convolution with the kernel and provided with more training data.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11591/eecsi.v6i0.2013">doi:10.11591/eecsi.v6i0.2013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3ulm6val3jfjvkhlahngzgk3i4">fatcat:3ulm6val3jfjvkhlahngzgk3i4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200507051336/http://journal.portalgaruda.org/index.php/EECSI/article/download/2013/1458" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4a/f8/4af8df90bd1fac609fa6ad48f3e126158a2c93dc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.11591/eecsi.v6i0.2013"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Very Efficient Training of Convolutional Neural Networks using Fast Fourier Transform and Overlap-and-Add

Tyler Highlander, Andres Rodriguez
<span title="">2015</span> <i title="British Machine Vision Association"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/6bfo5625nvdfvbgyf7ldi5wmfe" style="color: black;">Procedings of the British Machine Vision Conference 2015</a> </i> &nbsp;
Convolutional neural networks (CNNs) are currently state-of-the-art for various classification tasks, but are computationally expensive.  ...  Convolution can be efficiently performed as a Hadamard product in the frequency domain. The bottleneck is the transformation which has a cost of O(N 2 log 2 N) using the fast Fourier transform (FFT).  ...  In Proceedings of the ACM International Conference on Multimedia, pages 675-678, 2014. [2] Michael Mathieu, Mikael Henaff, and Yann LeCun. Fast training of convolutional networks through FFTs.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5244/c.29.160">doi:10.5244/c.29.160</a> <a target="_blank" rel="external noopener" href="https://dblp.org/rec/conf/bmvc/HighlanderR15.html">dblp:conf/bmvc/HighlanderR15</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/rzxphphf3zazxc7al74ibpcbym">fatcat:rzxphphf3zazxc7al74ibpcbym</a> </span>
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Pattern Detection Model Using a Deep Learning Algorithm for Power Data Analysis in Abnormal Conditions

Jeong-Hee Lee, Jongseok Kang, We Shim, Hyun-Sang Chung, Tae-Eung Sung
<span title="2020-07-14">2020</span> <i title="MDPI AG"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ikdpfme5h5egvnwtvvtjrnntyy" style="color: black;">Electronics</a> </i> &nbsp;
in advance by using the hybrid Convolutional Neural Networks (CNN)–Long Short-Term Memory (LSTM) algorithm, and the Fast Fourier Transform (FFT) technique.  ...  We found that it is easier to detect abnormal patterns that cannot be found in the existing time domain after preprocessing the data set through FFT.  ...  In this paper, we tried to address these issues by the proposed hybrid CNN-LSTM algorithm and the Fast Fourier Transform (FFT) technique, where we perform the preprocessing of the data set through FFT,  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/electronics9071140">doi:10.3390/electronics9071140</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3xe6zmikk5h3xiuh7ez3patimy">fatcat:3xe6zmikk5h3xiuh7ez3patimy</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200722111058/https://res.mdpi.com/d_attachment/electronics/electronics-09-01140/article_deploy/electronics-09-01140.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/a0/ee/a0eedf90af85b7aca0499487ce0fe32271195cc6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3390/electronics9071140"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> mdpi.com </button> </a>

Encoding Rich Frequencies for Classification of Stroke Patients EEG Signals

Fawaz Sammani, Kok Swee Sim, Shing Chiang Tan
<span title="">2020</span> <i title="Institute of Electrical and Electronics Engineers (IEEE)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/q7qi7j4ckfac7ehf3mjbso4hne" style="color: black;">IEEE Access</a> </i> &nbsp;
In particular, our model consists of several sub-modules which convert and re-model widely used signal processing techniques such as the Fast Fourier Transform (FFT), Convolution in the Frequency Domain  ...  and the Inverse Fast Fourier Transform (IFFT) to learnable and differentiable functions that are completely learned and optimized in an end-to-end manner by neural networks.  ...  LEARNING THE FREQUENCY CONVOLUTION AND THE FAST FOURIER TRANSFORM We first re-visit the Fast Fourier transform (FFT) and the Inverse Fast Fourier transform (IFFT).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/access.2020.3011185">doi:10.1109/access.2020.3011185</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/no6vy26l5fbabixf4l4vex5kau">fatcat:no6vy26l5fbabixf4l4vex5kau</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210717151653/https://ieeexplore.ieee.org/ielx7/6287639/8948470/09145945.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2d/41/2d41268ee80b1b6fef84735c274fd59377872b5c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1109/access.2020.3011185"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> ieee.com </button> </a>

Gesture Recognition Using LFMCW Radar and Convolutional Neural Network

Peng-hui CHEN, Yu-jing BAI, Jun WANG
<span title="2019-11-25">2019</span> <i title="DEStech Publications"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/52spf3of4jbu5da2xrhvubclcy" style="color: black;">DEStech Transactions on Computer Science and Engineering</a> </i> &nbsp;
The R-D map series is taken as the three dimensional convolutional neural network (3D-CNN) input samples, and the gesture features are extracted via convolution layer and pooling layer, and the gesture  ...  To explore the application of the extracted gesture features, a 77GHz radar system is applied, and six kinds of gestures are designed to verify the performance of classification and recognition.  ...  periods and perform fast Fourier transformation (FFT) to the frequency domain.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12783/dtcse/cscme2019/32550">doi:10.12783/dtcse/cscme2019/32550</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/7a5ljyjtvvdz5lez3u6qna3gva">fatcat:7a5ljyjtvvdz5lez3u6qna3gva</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200505054358/http://dpi-proceedings.com/index.php/dtcse/article/download/32550/31140" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/94/2e/942e4e1d5b76bd32c0530c94ee63a7b4ec48091d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.12783/dtcse/cscme2019/32550"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

Application Research on Optimization Algorithm of sEMG Gesture Recognition Based on Light CNN+LSTM Model

Dianchun Bai, Tie Liu, Xinghua Han, Hongyu Yi
<span title="2021-11-08">2021</span> <i title="American Association for the Advancement of Science (AAAS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/sn4cdxkepzdiniytgjqwnszm7q" style="color: black;">Cyborg and Bionic Systems</a> </i> &nbsp;
The feature model is established by using multidimensional sequential sEMG images by combining convolutional neural network and long-term memory network to solve the problem of multistate sEMG signal recognition  ...  In order to ensure the high accuracy of deep learning in multistate muscle action recognition and ensure that the training model can be applied in the embedded chip with small storage space, this paper  ...  Acknowledgments The authors thank the Laboratory 107, School of Electrical Engineering, Shenyang University of Technology, for the experimental platform provided; the authors also thank the volunteers  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.34133/2021/9794610">doi:10.34133/2021/9794610</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/t4iaroco3rgnpnw6xzbix7xeqi">fatcat:t4iaroco3rgnpnw6xzbix7xeqi</a> </span>
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Development of Deep Convolutional Neural Network with Adaptive Batch Normalization Algorithm for Bearing Fault Diagnosis

Chao Fu, Qing Lv, Hsiung-Cheng Lin
<span title="">2020</span> <i title="Hindawi Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/5k6wnnhj5fbe7o7v3zavqqtk4u" style="color: black;">Shock and Vibration</a> </i> &nbsp;
and Deep Neural Network with Fast Fourier Transform (FFT-DNN).  ...  Many previous works using a deep convolutional neural network (CNN) have achieved excellent performance in finding fault information from feature extraction of detected signals.  ...  Acknowledgments is work was supported by the Key Fund of Hebei Provincial Education Department (Grant no. ZD2018028).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2020/8837958">doi:10.1155/2020/8837958</a> <a target="_blank" rel="external noopener" href="https://doaj.org/article/92b2d4129eda47d6972e3b662dc978f6">doaj:92b2d4129eda47d6972e3b662dc978f6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nzubgw5qsjfk7h7h7mvifluxam">fatcat:nzubgw5qsjfk7h7h7mvifluxam</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20201103222315/http://downloads.hindawi.com/journals/sv/2020/8837958.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fa/68/fa68b6948d79cea713bbbd3d219ed23bb60fc959.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1155/2020/8837958"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> hindawi.com </button> </a>

Deep Residual Fourier Transformation for Single Image Deblurring [article]

Xintian Mao, Yiming Liu, Wei Shen, Qingli Li, Yan Wang
<span title="2021-11-23">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this paper, we present a Residual Fast Fourier Transform with Convolution Block (Res FFT-Conv Block), capable of capturing both long-term and short-term interactions, while integrating both low- and  ...  With Res FFT-Conv Block, we further propose a Deep Residual Fourier Transformation (DeepRFT) framework, based upon MIMO-UNet, achieving state-of-the-art image deblurring performance on GoPro, HIDE, RealBlur  ...  FFC denotes replacing Res FFT-Conv Block in DeepRFT by fast Fourier convolutions [41].  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.11745v1">arXiv:2111.11745v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/qp6ijrg3lnadlf7vmqbmgdbtiu">fatcat:qp6ijrg3lnadlf7vmqbmgdbtiu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211130174048/https://arxiv.org/pdf/2111.11745v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/3c/5a/3c5ab1aba2091c690729b5a8f0762ecda3d06163.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.11745v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

CircConv: A Structured Convolution with Low Complexity [article]

Siyu Liao, Zhe Li, Liang Zhao, Qinru Qiu, Yanzhi Wang, Bo Yuan
<span title="2019-02-28">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
cost by using fast multiplication of the circulant tensor.  ...  Through extensive experiments, such strong structure-imposing approach is proved to be able to substantially reduce the number of parameters of convolutional layers and enable significant saving of computational  ...  Since multiplication is the kernel computation in neural network training and inference, the existence of fast multiplication of circulant tensor enables the immediate reduction in computational cost.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.11268v1">arXiv:1902.11268v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3xrjcovhm5boll7hsan4evtpfm">fatcat:3xrjcovhm5boll7hsan4evtpfm</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200914205757/https://arxiv.org/pdf/1902.11268v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fb/45/fb45445db753c4234cdcae065d0aa9c8ee460823.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.11268v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Face Recognition with Hybrid Efficient Convolution Algorithms on FPGAs [article]

Chuanhao Zhuge, Xinheng Liu, Xiaofan Zhang, Sudeep Gummadi, Jinjun Xiong, Deming Chen
<span title="2018-03-23">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work, we explore different fast convolution algorithms including Winograd and Fast Fourier Transform (FFT), and find an optimal strategy to apply them together on different types of convolutions  ...  Deep Convolutional Neural Networks have become a Swiss knife in solving critical artificial intelligence tasks.  ...  ACKNOWLEDGMENTS This work is supported by IBM-Illinois Center for Cognitive Computing Systems Research (C 3 SR), a research collaboration as part of the IBM AI Horizons Network.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.09004v1">arXiv:1803.09004v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/5vs3hyqbl5ec7acd4yfh3abic4">fatcat:5vs3hyqbl5ec7acd4yfh3abic4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200902073208/https://arxiv.org/pdf/1803.09004v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/81/d4/81d46b8eb05d2ee67e67ee18351fcef7c629712d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1803.09004v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Band-limited Training and Inference for Convolutional Neural Networks [article]

Adam Dziedzic and John Paparrizos and Sanjay Krishnan and Aaron Elmore and Michael Franklin
<span title="2019-11-21">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The convolutional layers are core building blocks of neural network architectures. In general, a convolutional filter applies to the entire frequency spectrum of the input data.  ...  We explore artificially constraining the frequency spectra of these filters and data, called band-limiting, during training.  ...  This research was supported in part by the Center for Unstoppable Computing (CERES) at University of Chicago, NSF CISE Expeditions Award CCF-1139158, generous support from Google and NVIDIA, and the NSF  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.09287v1">arXiv:1911.09287v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/kqowv5qxl5fvrkcpfcalmj2nmu">fatcat:kqowv5qxl5fvrkcpfcalmj2nmu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200831143811/https://arxiv.org/pdf/1911.09287v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/7b/67/7b67493872683ba3eff8cf906c4b95592cb4a302.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1911.09287v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Project for Developing a Linear Algebra Library for High-Performance Computers [chapter]

J. Demmel, J. Dongarra, J. DuCroz, A. Greenbaum, S. Hammarling, D. Sorensen
<span title="">1989</span> <i title="Springer US"> Solution of Superlarge Problems in Computational Mechanics </i> &nbsp;
Dense Linear Algebra (DLA) is needed in a wide variety of science and engineering applications: • Linear systems: Solve Ax = b • Computational electromagnetics, material science, applications using boundary  ...  are typically 3D volumes Ø Handled through tensors Convolution Network (ConvNet) example Ø Convolutions can be accelerated in various ways: Ø Unfold and GEMM Ø FFT Ø Winograd minimal filtering  ...  ( X ) ≈ s 1 X1 + s 2 X2 Small matrices, tensors, and batched computations Ø Convolutions D i,c * G k,c of images D i,c and filers G k,c can be accelerated through FFT, as shown by the following equality  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4613-0535-4_4">doi:10.1007/978-1-4613-0535-4_4</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bwi3sek6qfahfllclcxkgel5cu">fatcat:bwi3sek6qfahfllclcxkgel5cu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200319222604/https://www.icl.utk.edu/files/publications/2019/icl-utk-1228-2019.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/2c/00/2c00f8d7d942f1bd987d5884f3d99242aa904425.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-1-4613-0535-4_4"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>
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